# Tagged Questions

The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

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### Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and no torque is acting?

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to ...
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### Why does the magnitude of linear momentum of a particle in circular motion change with radius? [duplicate]

My problem is with linear momentum of a particle in circular motion. If we imagine a particle moving around a circle, if there are no torques acting, then we can say its angular momentum is conserved, ...
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### Spin Orbital Coupling matrix in p-orbital basis

So I have the following Hamiltonian inherited from atomic Physics: $H_{SOC}=\alpha \vec{L}\cdot \vec{S}=\frac{\alpha}{2}(L^{+}\sigma^{+}+L^{-}\sigma^{-}+ L^{z}\sigma^{z})$ Where L is the angular ...
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### Spheres collide with merry-go-round [closed]

Four spheres, with uniform densities $\rho_1, \rho_2, \rho_3, \rho_4$ and radii $r_1, r_2, r_3, r_4$, respectively, roll without slipping with constant velocities $v_1, v_2, v_3, v_4$ along tracks ...
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### Angular momentum in rolling about the point of contact

A cylinder of mass 5 kg and radius 10 cm is moving on a horizontal surface with velocity of centre of mass 5 m/s towards right and angular speed 10 rad/s (clockwise) . Find the angular momentum of the ...
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### Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
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### Mechanics of a falling cat [duplicate]

It is a general statement that cats tend to fall on their feet. How far is this is a valid statement? If I were to drop a cat from 50 meters height, feet up(hypothetically), would it still land on ...
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### Could an asteroid land slowly on Earth's surface?

The concept in my mind is that an asteroid is on a vector similar to Earth's, but slightly slower (e.g., 50kmh slower). As Earth passes it, it enters the atmosphere at a sharp angle, and since Earth ...